A new failure times model for one and two failure modes system: A Bayesian study with Hamiltonian Monte Carlo simulation

Abba, Badamasi; Wang, Hong

doi:10.1177/1748006x221146367

Cited by 5 publications

(5 citation statements)

References 49 publications

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“…In this study, the parameters γ, α, θ , and λ are supposed to have gamma priors following the works of Kundu Howlader [48], Soliman et al [49], and Abba and Wang [29]. Let π(ϕ k ) denote the gamma prior having (ν k , γ k ) as the hyper-parameters, with PDF given by…”

Section: Bayesian Estimationmentioning

confidence: 99%

“…Calculating the Bayes estimates (BEs) via the posterior means may be infeasible with no closed-form solutions of the marginal posterior densities π(α|D), π(γ|D), π(λ|D), and π(θ|D). Hence, we opt for NUTS [50], another form of the HMC algorithm, to samples from the posterior distribution using Rstan [51] in R. A recent re-explanation of the HMC algorithm can be found in [29]. VOLUME 11, 2023 Hence, for a posterior sample {ϕ s , s = 1, 2, .…”

Section: Bayesian Estimationmentioning

confidence: 99%

“…On the other hand, several extension of Weibull distribution with similar physical interpretation to EW distribution are defined. These include the new modified Weibull [22], additive modified Weibull [23], Weibull Lindley [24], log-normal modified Weibull [15], improved new modified Weibull [25], Weibull-Chen [26], additive Chen Weibull [27], flexible additive Chen-Gompertz [28], and additive Gompertz-Weibull [29] distributions.…”

Section: Introductionmentioning

confidence: 99%

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A New Flexible Four Parameter Bathtub Curve Failure Rate Model, and Its Application to Right-Censored Data

et al. 2023

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This article introduces a new flexible four parameter distribution by convolution of the exponential and Weibull distribution using the odd function transformation, which offers greater flexibility in terms of fit, its called the modified exponential-Weibull (MEW). The MEW model is designed to provide a more accurate description of failure time data resulting from a system with one or more failure modes and is characterized by a hazard rate (HR) that takes the shape of a bathtub due to its complexity. The moments properties, quantile function, and residual life are derived and discussed. We discussed the HR function and several distributional properties of the MEW model, and applied maximum likelihood and Bayesian techniques to estimate its unknown parameters. The Hamiltonian Monte Carlo (HMC) algorithm is employed to simulate the posterior distributions and verify the MEW Bayes estimators. We examined the behavior of the MEW model on two data sets with bathtub-shaped HR and compare it with five other popular bathtub-shaped methodologies. The results indicate that the MEW model provided the best description of the two failure time data sets, suggesting that the proposed model could be a viable candidate for solving various real-life problems.INDEX TERMS Bathtub-shape hazard rate, exponential-Weibull model, moments, residual life, Hamiltonian Monte Carlo simulation, time to failure data.

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Section: Bayesian Estimationmentioning

confidence: 99%

Section: Bayesian Estimationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A New Flexible Four Parameter Bathtub Curve Failure Rate Model, and Its Application to Right-Censored Data

et al. 2023

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“…In reliability settings, notably in repair and replacement plans, the MRL appears to offer more reliability information than the HRF. 12,13 This is because, at time 𝑡, the MRL describes the entirety of the remaining FT beyond 𝑡, while at the same time, the HRF offers information on a device's or an individual's failure in a brief window after 𝑡.…”

Section: Mean Residual Lifementioning

confidence: 99%

A two‐parameter parsimonious bathtub model for the analysis of system failure times with illustrations to reliability data

Bakouch,

Abba,

Jónás

et al. 2023

Quality & Reliability Eng

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In this study, a two‐parameter, upper‐bounded probability distribution called the tau distribution is introduced and its applications in reliability engineering are presented. Each of the parameters of the tau distribution has a clear semantic meaning. Namely, one of them determines the upper bound of the distribution, while the value of the other parameter influences the shape of the cumulative distribution function. A remarkable property of this new probability distribution is that its probability density function, survival function, hazard rate function (HRF), and quantile function can all be expressed in terms of its cumulative distribution function. The HRF of the proposed probability distribution can exhibit an increasing trend and various bathtub shapes with or without a low and long‐flat phase (useful time phase), which makes this new distribution suitable for modeling a wide range of real‐world problems. The constraint maximum likelihood estimation, percentile estimation, approximate Bayesian computation, and approximate quantile estimation computation are proposed to calculate the unknown parameters of the model. The suitability of the estimation methods is verified with the aid of simulation and real‐world data results. The modeling capability of the tau distribution was compared with that of some well‐known two‐ and three‐parameter probability distributions using two data sets known from the literature of reliability engineering: time between failures data of a machining center, and time to failure of data acquisition system cards. Based on empirical results, the new distribution may be viewed as a viable competitor to the Weibull, Gamma, Chen, and modified Weibull distributions.

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“…1, cutting time and cutting tool flank wear are selected as the horizontal and vertical coordinates respectively. The wear process of cutting tools can be divided into three stages: initial wear stage, normal wear stage and rapid wear stage [38]. In this subsection, a theoretical basis for the segmentation of the degradation process of the cutting tool is presented.…”

Section: The Degradation Process Of Cutting Toolsmentioning

confidence: 99%

Cutting tool wear prediction based on the multi-stage Wiener process

Wang,

Chang,

Huang

et al. 2023

Int J Adv Manuf Technol

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Cutting tools are one type of the critical components of the modern computer numerical control (CNC) machining system, whose failure can lead the whole system to fail or even cause substantive losses. Therefore, it is of great importance to study the method for tool wear prediction. A new model for wear prediction of cutting tools is established based on a multi-stage Wiener process, where the degradation rates of cutting tools are considered to change in three stages based on the typical cutting tool wear curve model. Firstly, the degradation processes of cutting tools are divided into three stages.Secondly, the parameter estimation for each stage of the degradation processes of cutting tools is completed respectively by utilizing the EM (expectation-maximization) algorithm. Then, the wear of cutting tools is predicted, and the reliability of cutting tools is analyzed by using a numerical integration simulation method based on the Monte Carlo algorithm. Finally, the proposed model is illustrated and verified via the flank wear data of cutting tools, and the prediction accuracy is measured by mean squared error (MSE) and the coefficient of determination ( 2R ). The prediction results show that the proposed model enables us to make more economical maintenance by delaying the tool replacement time with fewer degradation data. And compared to the traditional methods based on machine learning (ML), the proposed model can complete the wear prediction and reliability analysis more accurately.

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A new failure times model for one and two failure modes system: A Bayesian study with Hamiltonian Monte Carlo simulation

Cited by 5 publications

References 49 publications

A New Flexible Four Parameter Bathtub Curve Failure Rate Model, and Its Application to Right-Censored Data

A New Flexible Four Parameter Bathtub Curve Failure Rate Model, and Its Application to Right-Censored Data

A two‐parameter parsimonious bathtub model for the analysis of system failure times with illustrations to reliability data

Cutting tool wear prediction based on the multi-stage Wiener process

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